Reduction of Taylor dispersion in a capillary by spin-up flow—Theoretical insights

Abstract

We have developed a theoretical framework to characterize the transport and mixing of a passive scalar in a capillary tube. In this configuration, a suspension of magnetic nanoparticles undergoes Poiseuille flow, while a rotating magnetic field is applied around the tube’s revolution axis, inducing a secondary flow in the azimuthal direction. This secondary flow facilitates the mitigation of concentration gradients and radial dispersion associated with the axial parabolic Poiseuille profile. The improvement in mixing is emphasized by a new dimensionless parameter, the mixing factor, which is incorporated into the scalar transport equation. Such a factor acts as a quantitative measure of the effect of the tangential motion induced by the spin-up flow on the overall mixing efficiency of the liquid and the observed reduction of the Taylor dispersion in the measured residence time distributions. Recognizing the mixing factor as a crucial parameter advances our understanding of the mechanisms governing scalar transport and provides a valuable tool for predicting and optimizing mixing in laminar capillary flows subjected to spin-up motion.